A193084 Decimal expansion of the coefficient of x in the reduction of (e^x)*cos(x) by x^2->x+1.

3, 0, 2, 9, 5, 8, 8, 7, 1, 4, 3, 3, 6, 2, 6, 0, 0, 1, 1, 9, 7, 5, 8, 4, 9, 8, 0, 2, 3, 5, 4, 8, 1, 1, 3, 6, 5, 2, 9, 3, 9, 1, 8, 9, 2, 1, 9, 5, 4, 7, 5, 9, 8, 1, 0, 0, 5, 2, 4, 4, 4, 4, 7, 6, 5, 9, 5, 1, 2, 9, 6, 5, 6, 8, 4, 9, 8, 4, 8, 7, 2, 3, 9, 3, 2, 3, 1, 0, 8, 4, 8, 6, 2, 6, 2, 0, 4, 0, 7, 1

Offset: 0

Author

Clark Kimberling, Jul 15 2011

Keywords

• nonn
• cons

Comments

Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.

Examples

			-0.3029588714336260011975849802354811365293918921...
		

Crossrefs

Cf. A193010, A192232, A193083.

Programs

Mathematica

f[x_] := Exp[x] Cos[x]; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
RealDigits[u0, 10]  (* A193083 *)
u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
RealDigits[u1, 10]  (* A193084 *)